Graph 3x-5y=6

$3 x - 5 y = 6$

Step 1

Solve for $y$ .

Subtract $3 x$ from both sides of the equation.

$- 5 y = 6 - 3 x$

Divide each term in $- 5 y = 6 - 3 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = 6 - 3 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{6}{- 5} + \frac{- 3 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{6}{- 5} + \frac{- 3 x}{- 5}$

Divide $y$ by $1$ .

$y = \frac{6}{- 5} + \frac{- 3 x}{- 5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{6}{5} + \frac{- 3 x}{- 5}$

Dividing two negative values results in a positive value.

$y = - \frac{6}{5} + \frac{3 x}{5}$

Step 2

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Reorder $- \frac{6}{5}$ and $\frac{3 x}{5}$ .

$y = \frac{3 x}{5} - \frac{6}{5}$

Reorder terms.

$y = \frac{3}{5} x - \frac{6}{5}$

Step 3

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{3}{5}$

$b = - \frac{6}{5}$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{3}{5}$

y-intercept: $(0, - \frac{6}{5})$

Slope: $\frac{3}{5}$

y-intercept: $(0, - \frac{6}{5})$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Write in $y = m x + b$ form.

Reorder $- \frac{6}{5}$ and $\frac{3 x}{5}$ .

$y = \frac{3 x}{5} - \frac{6}{5}$

Reorder terms.

$y = \frac{3}{5} x - \frac{6}{5}$

Find the x-intercept.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{3}{5} x - \frac{6}{5}$

Solve the equation.

Rewrite the equation as $\frac{3}{5} x - \frac{6}{5} = 0$ .

$\frac{3}{5} x - \frac{6}{5} = 0$

Combine $\frac{3}{5}$ and $x$ .

$\frac{3 x}{5} - \frac{6}{5} = 0$

Add $\frac{6}{5}$ to both sides of the equation.

$\frac{3 x}{5} = \frac{6}{5}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 x = 6$

Divide each term in $3 x = 6$ by $3$ and simplify.

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

Find the y-intercept.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{3}{5} \cdot (0) - \frac{6}{5}$

Solve the equation.

Multiply $\frac{3}{5}$ by $0$ .

$y = \frac{3}{5} \cdot 0 - \frac{6}{5}$

Remove parentheses.

$y = \frac{3}{5} \cdot (0) - \frac{6}{5}$

Simplify $\frac{3}{5} \cdot (0) - \frac{6}{5}$ .

Multiply $\frac{3}{5}$ by $0$ .

$y = 0 - \frac{6}{5}$

Subtract $\frac{6}{5}$ from $0$ .

$y = - \frac{6}{5}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{6}{5})$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & - \frac{6}{5} \\ 2 & 0 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $\frac{3}{5}$

y-intercept: $(0, - \frac{6}{5})$

$\begin{array}{c} x & y \\ 0 & - \frac{6}{5} \\ 2 & 0 \end{array}$

Step 6

Graph 3x-5y=6

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